Quantum behaved PSO with Global best strategy in Characteristic Length to Explore the Solution Space Efficiently and Effectively

The characteristic length of the potential well largely determines the exploration in Quantum Particle Swarm Optimization. Previous methods calculated this length based on the mean of self-best solutions, resulting in slow convergence and accuracy issues due to symmetrical exploration. This work introduces a modified characteristic length that incorporates the globally best solution, enabling asymmetrical exploration around local attractors. This new approach allows for three levels of exploration in parallel: particles close to the global best focus on local refinement, those farther away contribute to global exploration, and others explore intermediate regions. By varying exploration depths, the algorithm improves convergence toward global optima. Various potential wells—including the Delta and Harmonic Oscillator—were analyzed to assess their effectiveness at guiding solution searches. As dimensionality increases, the challenge of lagging particles worsens when using the mean-based characteristic length, making the proposed global best-based approach more effective. To better evaluate algorithm performance, both accuracy and convergence characteristics are considered simultaneously, leading to the introduction of a new normalized distance measure. Extensive experiments using numerical optimization benchmark functions demonstrate that the global best-based characteristic length in the quantum version consistently outperforms the mean self-best-based approach. This trend was observed across multiple potential wells, indicating broad applicability. The Delta potential well that achieved the highest performance among all tested potential wells, for 19 functions from the CEC2005 benchmark, normalized accuracy increased by 6.8% and convergence characteristics improved by 66.62%. For 28 functions from CEC2017, performance improved by 14.29% compared to the Farmer and Seasons Algorithm. These experimental results indicate that the global best-based characteristic length significantly enhances solution exploration and convergence. Additionally, the proposed quality measurement index enables more accurate algorithm comparison. Research has also been carried out to exploring the solution space using multiple potential wells and benefits has been estimated compared to single potential well.